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Pertanyaan

Tentukan polinomial begin mathsize 14px style p left parenthesis x right parenthesis end style dan begin mathsize 14px style q left parenthesis x right parenthesis end style dengan ketentuan berikut.

a. undefined dan undefined berderajat 4 dengan syarat begin mathsize 14px style p left parenthesis x right parenthesis plus q left parenthesis x right parenthesis end style berderajat 3.

A. Damanhuri

Master Teacher

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Jawaban

polinomial undefined dan undefined.

Pembahasan

Misal:

 begin mathsize 14px style p left parenthesis x right parenthesis equals a x to the power of 4 plus b x cubed plus c x squared plus d x plus e q open parentheses x close parentheses equals negative a x to the power of 4 plus b x cubed plus c x squared plus d x plus e end style 

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p open parentheses x close parentheses plus q open parentheses x close parentheses end cell equals cell open parentheses a x to the power of 4 plus b x cubed plus c x squared plus d x plus e close parentheses plus left parenthesis negative a x to the power of 4 plus b x cubed plus c x squared plus d x plus e right parenthesis end cell row blank equals cell a x to the power of 4 minus a x to the power of 4 plus b x cubed plus b x cubed plus c x squared plus c x squared plus d x plus d x plus e plus e end cell row blank equals cell 2 b x cubed plus 2 c x squared plus 2 d x plus 2 e end cell end table end style 

Contoh:

Misal begin mathsize 14px style p left parenthesis x right parenthesis equals x to the power of 4 plus x cubed plus x squared plus x plus 1 end style dan begin mathsize 14px style q left parenthesis x right parenthesis equals negative x to the power of 4 plus x cubed plus x squared plus x plus 2 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p left parenthesis x right parenthesis plus q left parenthesis x right parenthesis end cell equals cell left parenthesis x to the power of 4 plus x cubed plus x squared plus x plus 1 blank right parenthesis plus left parenthesis negative x to the power of 4 plus x cubed plus x squared plus x plus 2 right parenthesis end cell row blank equals cell x to the power of 4 minus x to the power of 4 plus x cubed plus x cubed plus x squared plus x squared plus x plus x plus 1 plus 2 end cell row blank equals cell 2 x cubed plus 2 x squared plus 2 x plus 3 end cell row blank blank blank end table end style   

Jadi, polinomial undefined dan undefined.

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